 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-1/6/ii/c/solution

The coordinate

x_{1}^{'}

does not occur. The perpendicular cross-section is

\frac{x _{2}^{'2}}{k / λ _{2}} + \frac{x _{3}^{'2}}{k / λ _{3}} = 1.

Thus the surface is an elliptic cylinder extending in both directions along the zero-eigenvalue axis. Its cross-sectional semiaxes are

k / λ_{2}

and

k / λ_{3}

. It becomes a circular cylinder when the two positive eigenvalues coincide.

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